{"paper":{"title":"Linear Probing with Non-Greedy Insertions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrew Krapivin, Jolyne Wang, William Kuszmaul","submitted_at":"2026-07-20T02:53:18Z","abstract_excerpt":"Linear probing hash tables classically use a \\emph{greedy} insertion strategy, placing a key $u$ in the first available position out of $h(u), h(u) + 1, h(u) + 2, \\ldots$. If the hash table is filled to $1 - 1/x$ full, this results in $\\Theta(x^{2})$ worst-case expected insertion time.\n  In this note, we show that there is a simple \\emph{non-greedy} insertion strategy that does better, and without requiring elements to be reordered within the table over time. Given $x$ in advance, the strategy is able to bring the worst-case expected insertion time down to $O(x \\log x)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17494","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.17494/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}